Observation of flow vector fluctuations in p$-$Pb collisions at $\mathbf{\sqrt{\textit{s}_{_{\bf NN}}}}=$ 5.02 TeV

Measurements of transverse momentum ($p_{\rm T}) and pseudorapidity ($\eta$) dependent flow vector fluctuations in p--Pb collisions at $\sqrt{s_{\rm NN}} = 5.02 TeV at the CERN Large Hadron Collider are presented. Utilizing long-range two-particle correlations with the template fit method, potential biases from non-flow effects such as jets and resonance decays are effectively suppressed. Significant $p_{\rm T}$ and $\eta$ dependent fluctuations of the second-harmonic flow vector are observed with more than $5\sigma$ confidence in p--Pb collisions, mirroring observations in Pb--Pb collisions. These results cannot be solely attributed to non-flow effects, providing new evidence for flow vector fluctuations in small collision systems at the LHC. Comparisons with hydrodynamic model calculations from 3DGlauber+MUSIC+UrQMD and parton transport model calculations from AMPT significantly enhance the understanding of the three-dimensional initial geometry and its event-by-event fluctuations, offering critical insights into the origin of collective flow in small collision systems at the LHC.